Viscoelastic and Dielectric Relaxation Behavior of Substituted Poly(p

Macromolecules 1995,28, 1872-1881

1872

Viscoelastic and Dielectric Relaxation Behavior of Substituted Poly(ppheny1enes) Michael Connolly and Frank Karasz* Department of Polymer Science & Engineering, University of Massachusetts, Amherst, Massachusetts 01003

Mark Trimmer Maxdem Incorporated, 140 East Arrow Highway, San Dimas, California 91 773 Received November 8, 1994; Revised Manuscript Received January 4, 1995@

ABSTRACT: The thermal, dynamic mechanical, and dielectric relaxation behavior of poly@-phenylenes) substituted with benzoyl and 4-phenoxybenzoyl groups and of a copolymer of benzoyl-l,4-phenylene and 1,a-phenylene were investigated. These amorphous materials were found to have flexural moduli higher than any other reported unoriented thermoplastic. Benzoyl-substituted poly(p-phenylene)which possesses the greatest rigid-rod character also displayed the highest modulus. The temperature dependence of viscoelastic and dielectric relaxation times were well described by the Williams-Landel-Ferry and VogelFulcher equations, respectively. The temperature sensitivity or “fragility”of viscoelastic shift factors aT and apparent dielectric relaxation times t* was greatest for the copolymer. The glass transition temperature of these polymers varied as a function of the total free volume. The polymer containing the 4-phenoxybenzoyl side group exhibited the lowest Tgdue to internal plasticization, but the highest Vogel energy attributable to the large intramolecular bond rotational barrier associated with the bulky pendant group. The shape of frequency plane dielectric relaxation spectra of the substituted polyphenylenes could be accurately fitted t o the Kolrausch-Williams-Watts (KWW) correlation function. The KWW stretched exponential term j3 displayed a very weak dependence on molecular structure and remained constant within experimental error for each material over the temperature range studied. Since j3 should be proportional t o the degree of intermolecular coupling, the structural variation in “fragility”,albeit small, of the substituted polyphenylenes may not be fully described by the coupling model for relaxation. Assuming the macroscopic expansion coefficient is proportional to the free volume expansion coefficient, the temperature dependence o f t * and aT may be explained more simply from free volume considerations. The 4-phenoxybenzoyl-substituted polymer displayed the highest expansion coefficient and largest total coDolvmer exhibited the largest relative change free volume, but the benzovl-1,4-~henvlene/l.3-~henvlene - . in free volume with temperature, wk;ich explained the greate; “fragility” of the copiymer compared t o either homopolymer.

I. Introduction Engineering thermoplastics continue to find new applications and ofien replace traditional structural materials of metal and ceramic. It is empirically observed that incorporation of a large fraction of main chain aromatic groups in a polymer imparts high temperature stability. Unfortunately, the aromatic nature of polymers such as poly@-phenylene)results in highly crystalline, insoluble, and infusible materials which are thereby excluded from use in structural applications. To optimally balance material performance and processing characteristics, research groups have studied systems which incorporated side chains on linear aromatic polymers including p~ly(p-phenylene).l-~ Recently, Marrocco and c o - w o r k e r ~ have ~ - ~ reported largescale synthesis of high molecular weight substituted polyphenylenes. They observed unusually high flexural moduli (approximately 10 GPa) for materials which were thermoplastic, remained soluble in common organic solvents after processing, and displayed no crystallinity detectable by DSC or X-ray analysis. In this contribution, we report on the thermal, dynamic mechanical, and dielectric relaxation behavior of poly(1,4-phenylenes)substituted with either benzoyl or 4-phenoxybenzoyl groups and a copolymer of benzoyl-

* To whom correspondence should be addressed.

Abstract published in Advance ACS Abstracts, February 15, 1995. @

1,Cphenylene with 1,3-phenylene in order to more fully understand their basic properties. We are interested particularly in the nature of segmental motions which are responsible for the glass t o rubber transition. In linear flexible and semiflexible polymers, the glass transition represents the onset of long range diffusive motions of chain backbone segments. The molecular structure of the repeat units controls this segmental motion. Polymers which contain small, flexible repeat units such as poly(oxymethy1ene)are limited in their segmental motion primarily by local bond rotational barriers and hence display symmetric, Debye-type relaxation spectra and a near-hrhenius temperature dependence of their relaxation times. Conversely, polymers with large, sterically hindered monomer segments such as Bisphenol A polycarbonate (BPA-PC) exhibit very broad, asymmetric relaxation spectra with relaxations times having a distinctly non-Arrhenius temperature dependence. Ngai and co-workers8-10 have attributed these effects of chemical structure to the intermolecular cooperativity or coupling of segmental motions with relaxations of neighboring, nonbonded segments. The rigid-rod nature of substituted polyphenylenes studied in this report provides an interesting new topology for evaluation of the concepts of the cooperativity model. 11. Experimental Section A. Materials. The benzoyl- and 4-phenoxybenzoyl-substituted poly(p-phenylenes)were supplied by Maxdem, Inc. (PX1000 and PX-2000, respectively) together with an experimental

0024-9297/95/2228-1872$09.00/00 1995 American Chemical Society

Macromolecules, Vol. 28, No. 6, 1995

Substituted Poly@-phenylenes)

0

&; 0'

PXW-1000

PXW-2Ooo

PoMbenzoyl- 1+phenylene)

Poly(4'-phenoxybenzoyl1,4-phenylene)

4

,c=o

P-1 Poly[(benzoyl- 1,Cphenylene)-ca- 1,3-phenylene] Figure 1. Structures of Poly-X polyphenylenes. Table 1. Characterizationof Poly-X Poly@-phenylenes) calculated wt % measured wt % sample C H C H PX-1000 86.68 4.44 87.10 4.53 83.99 4.41 83.83 4.41 PX-2000 P-1 87.24 4.50 87.97 4.51

85/15 (mol/mol %) benzoyl-1,4-phenylene/l,3-phenylene copolymer (P-1). The chemical structure of each material (Figure 1) was confirmed by elemental analysis and IR spectroscopy. Elemental analysis results (University of Massachusetts Microanalytical Laboratory) are reported in Table 1. The as-received powders were redissolved in chloroform (5 w t %) over a 24 h time period using mild heating and vigorous stirring. Samples were precipitated by slowly pouring the pale yellow chloroform solutions into a high-speed blender containing a 10-fold excess of methanol. The precipitate was collected in a fritted glass funnel, dried in vacuum for 12 h at room temperature, 24 h a t 80 "C, and finally at 120 "C for 12 h, and stored in uucuo. Bisphenol A polycarbonate (BPA-PC) pellets were used as-received (Aldrich). The weight average molecular weight (M,) of the BPA-PC was found to be 21 800 by static light scattering in THF a t 25 "C compared to a polystyrene calibrated GPC value of M , = 47 000, and molecular weight distribution (MWD) = 2.30 in THF a t 30 "C. Samples were prepared for analysis by compression molding in vacuum at 300 "C under approximately 3 metric tons of pressure. Powder samples of the Poly-X resins were initially sintered into solid slabs by placing the powder between Kapton sheets and compressing a t 300 "C for 30 s under 1metric ton pressure. Samples for dynamic mechanical analysis were formed by molding the sintered powders into rectangular bars 1 mm thick, 10 mm wide, and 30 mm long. To ensure formation of uniform and reproducible specimens, material placed between Kapton sheets was held in vacuum a t 300 "C for 5 min before applying pressure to achieve thermal equilibrium, annealed a further 15 min after molding to allow the sample to relax, and then cooled to 50 "C over a period of 10 min before removing from the vacuum chamber. Dielectric samples approximately 0.3 mm thick and 33 mm in diameter were prepared directly from the dry precipitate by placing approximately 0.3 g of polymer between Kapton sheets in a pellet type mold. Disks for dielectric analysis were molded under the same conditions as described for the dynamic mechanical samples, although 12 min was allowed for initial thermal equilibration due to the greater thermal mass of the mold. All samples remained soluble after compression molding.

1873

BPA-PC samples were molded at 200 "C by compressing the as-received pellets into the desired mold using the same thermal equilibration method as used for the Poly-X resins. B. Instrumental Methods. Sample degradation temperature and residual solvent content of the precipitated powders were determined using a Perkin-Elmer System 7 thermogravimetric analyzer (PE-TGA7). TGA experiments were performed on samples between 7 and 12 mg at 20 "C/ min under a dry nitrogen atmosphere from 30 to 900 "C. All poly@-phenylenes) studied exhibited less than 0.5% weight loss up to 300 "C, and this can be attributed to residual solvent and adsorbed water. Under dry Nz, 60-80 wt % char of the Poly-X resins remained a t 900 "C. Expansion coefficient measurements were obtained on a DuPont 2940 thermomechanical analyzer (TMA), calibrated with indium using a 2.54 mm diameter expansion probe under a 0.05 N load. Samples approximately 1mm thick were tested at 10 W m i n under dry Nz from 50 to 200 "C after cooling from 200 "C at 10 "C/min. The glass transition temperature (T,) was defined as the onset of the slope change in the expansion curves. Dynamic mechanical experiments were performed under dry nitrogen on a Polymer Laboratories DMTA Mk I in the single cantilever bending mode. Samples with a free length of 8 mm were constrained using a 0.30 Nm torque on each clamp nut. Thermal scans were made from -100 to f 2 5 0 "C at 2 "C/min a t 1,3, 10, and 30 Hz. Isothermal measurements were made at six frequencies between 0.1 and 30 Hz in 5 deg steps after allowing 6 min for the sample t o reach thermal equilibrium. Dielectric relaxation behavior was measured on a GenRad 1689M Digibridge which was interfaced with a Polymer Laboratories DETA Mk I system using an unguarded parallel plate cell of 31 mm diameter. Samples were sputter coated with gold and studied in thermal scans from -100 to +250 "C at 2 "C/min at 0.2, 1, 10, 28.5, and 100 kHz. Isothermal experiments were performed at 35 frequencies between 20 Hz and 100 kHz using 2-5 deg temperature intervals and 10 min thermal equilibration. Solutions of the copolymer (P-1)possessed much lower viscosities (vmh= 1.1d u g at 40 "C in 0.05 M LiBr/NMP using a Cannon-Ubbelodhe viscometer and a solution concentration of 0.10 g/dL) than the benzoyl- and 4-phenoxybenzoylsubstituted polymers (PX-1000 and PX-2000, respectively). To ensure that the low viscosity of P-1was due only to the flexible nature of the m-phenylene kink units, the M , of P-1 was determined by static light scattering using an Otsuka Electronics DLS-700 spectrophotometer which was calibrated with benzene (Aldrich Chemical Co., 99.9% HPLC grade) using a Rayleigh ratioll of 12.63 x cm-l. Samples were dissolved in chloroform (Aldrich Chemical Co., 99.8% ACS spectrophotometric grade) a t four concentrations between 1 and 5 mg/ mL and were filtered five times to remove dust using 0.22 pm Millipore FGS filters. All solvents were used as-received from the manufacturer. The refractive index increment with concentration (dnldc) of the P-1 light scattering solutions was measured using a n Otsuka Electronics RM-102 differential refractometer using a Brice-type split cell. Using a dnldc of 0.2628 f 0.004 at 25 "C, the M , of P-1 using a Zimm plot extrapolation was found to be 26 900 & 1000, indicating a weight average degree of polymerization of 164 f 6. The high viscosities of the homopolymer solutions precluded a meaningful M , measurement with available instrumentation. All Vogel-Fulcher and WLF fits of temperature dependent relaxation behavior were made using Kaleidagraph 3.0 graphics software (Abelbeck Software Inc.). The Kolrausch-Williams-Watts parameters AE and /3 were determined by comparing the shape of normalized dielectric loss spectra (E"/ t o the related probability density f u n c t i o n ~ . ~The ~J~ latter were calculated using a UNM-based program provided by the General Electric Co. Before analyzing the dielectric relaxation curves, the conductivity contribution E"cond to the loss was subtracted from the low-frequency side of the spectrum assuming ~ ' ' ~ ~=t ~6"dlpolar l + E'lcond and 6"cond = (2n,fRC&l where f i s the measurement frequency, R is the dc resistance, and COis capacitance of a n air gap equal to the sample thickness.


1874 Connolly et al.

m

a

E a

W

1o8

E0 3;

-2

io7 io9 L

W I I

2 v1

a

3

lo8

I +P-1

v1

io7 -100

-50

0

1II

-1wwu

50

100

I 150

200

250

Temperature ("C) Figure 2. Temperature dependence of (a) storage E' and (b) loss E moduli at 10 Hz for Poly-X polyphenylenes.

111. Results and Discussion

The dynamic mechanical behavior of the Poly-X resins over a wide temperature range is shown in Figure 2. The glassy moduli of these materials were found to be higher than any other reported amorphous thermoplasof 5.2, 6.0, and 7.6 GPa at 25 tic. Storage moduli (E') "C and 10 Hz for P-1, PX-2000, and PX-1000, respectively, agree well with the static flexural moduli of between 7 and 10 GPa reported p r e v i ~ u s l y . ~These ,~ values may be compared t o the flexural moduli of the amorphous engineering thermoplastics BPA-PC and BPA-polysulfone, 2.3 and 2.7 GPa, respectively. The rodlike polyphenylene backbone is capable of supporting large mechanical stresses, resulting in very high moduli even though these polymers are unoriented and noncrystalline. As expected, PX-1000 which possesses the greatest rigid-rod character exhibits the highest modulus while P-1 which contains nonlinear, "kink, units has the lowest modulus and highest d u ~ t i l i t y . ~It? ~ should be noted that the dynamic modulus described here is somewhat lower than that obtained in static flexural tests due to the relatively small sample size and finite instrumental compliance; the reproducibility of

the DMTA modulus measurements is better than f l GPa. The glass transition temperature (T,) of the polyphenylenes varies slightly with the substituent. PX-2000 which contains the largest side groups displays the lowest Tg of 150 "C, compared to 158 and 161 "C for PX-1000 and P-1, respectively. We expected initially that P-1 would possess the greatest mobility and lowest Tg since it incorporates m-phenylene units, disrupting the rigid-rod character of the p-phenylene backbone. Apparently, the large free volume induced by the bulky benzoyl and 4-phenoxybenzoyl side groups largely controls the segmental mobility of these polyphenylenes. As has been observed in alkyl methacrylate polymers, for example, increasing side-chain length results in an increase in free volume and a decrease of T p There appears to be little effect of the side group on the subambient mechanical relaxation behavior of the Poly-X materials. Only a very broad, weak relaxation is observed for all three polymers between -100 and +50 "C, indicating either that the side groups have restricted mobility in the glassy state or that the local relaxation modes do not significantly damp mechanical oscillations.


9.0

Substituted Poly@-phenylenes) 1876

b

8.0 7.0

+PP-1000

6.0 5.0

4.0

3.0

Figure 3. Temperature dependence of (a)dielectric permittivity E' and (b) dielectric loss E" at 10 kHz for Poly-X polyphenylenes.

As shown in Figure 3, a similar Tgtrend was observed in the dielectric measurements of the substituted polyphenylenes; Le., P-1 displays the highest Tg.Polymers such as poly(methy1methacryate) (PMMA)which contain strong dipoles in the side group typically also exhibit very strong local mode dielectric relaxations. PMMA shows only a weak mechanical ,b relaxation, but the magnitude of the dielectric/3 relaxation exceeds that of the Tgor a relaxation. In the polyphenylene family studied here, the strong dipoles of the benzoyl and 4-phenoxybenzoyl groups have only limited mobility in the glassy state; these materials display only weak local mode relaxations in the vicinity of -50 "C. The dipole moments of PX-1000 and PX-2000 repeat units are approximately equivalent to those of benzophenone @ = 2.98 D) and 4-phenoxybenzophenone @ 1.82 D).14 In the copolymer P-1, the average dipole moment may be regarded as the weighted average of benzophenone and benzene which has no dipole moment. Considering these approximations, the dielectric permittivity E' and relaxation strength A6 (the difference in e' above and below T g )of each of the Poly-X materials correlate with the strength and number of their respective polar side groups.

To more thoroughly probe the dynamics of these substituted polyphenylenes, the temperature dependence of the dynamic mechanical and dielectric relaxation spectra was determined using measurement conditions outlined above. For a system possessing a single relaxation mechanism, the temperature dependence of viscoelastic relaxation times has been described by the empirical Williams-Landel-Ferry (WLF)equation:15J6

where aT is the WLF shift factor, z* is the apparent relaxation time a t temperature T and is defined as 1/(2nf,,) with f m , equal t o the frequency of the mechanical loss (E")peak, ZR* is the apparent relaxation time at the reference temperature TR,and C1 and Cp are the WLF constants equal to B'/2.303f~and fdaf, respectively. B' is the Doolittle parameter on the order of unity, f R is the fractional free volume at TR,and afis the thermal expansion coefficient of the fractional free volume. The temperature dependence of the WLF shift factor aT is plotted in Figure 4 for each of the polyphenylene resins and the fit of each curve to the WLF



4.0 --e P P - l o 0 0

2.0 t$

0.0

0

I

-2.0 -4.0

150

130

170

190

Temperature ("C)

210

230

Figure 4. WLF plot of viscoelastic shift factors UT for all

Poly-X resins.

Table 2. WLF Parameters for Poly-X Mechanical Relaxation Behaviofl PX-2000 PX-1000 P-1

10.2 f 0.1 11.2 0.2 9.9 f 0.1

*

103.1 f 1.4 88.6 Z!Z 1.4 65.1 2~ 0.7

165 165 165

Determined by fitting the Williams-Landel-Ferry (eq 1) to the data in Figure 4. a

E + 2.303R(T - To)

2.10

2.20

2.30

2.40

1000/T (K-1) Figure 5. Arrhenius plot of apparent dielectric relaxation times t* for the a-relaxation of Poly-X resins. Table 3. Vogel-Fulcher Parameters for Poly-X Dielectric Relaxation Behavior

0.9999 0.9998 0.9999

equation

equation (eq 1)is recorded in Table 2. It is clear that PX-2000 exhibits a weaker temperature dependence of its relaxation time than either PX-1000 or P-1.The nature of this dependence will be discussed below. An alternative empirical expression describing the temperature dependence of relaxation times was introduced by Vogel17 and Fulcher:18 log t* = log to

2.00

(2)

where t* is the apparent relaxation time at temperature T from the mechanical (E") or dielectric (E") loss maximum, to is the primitive relaxation time at the Vogel temperature TOwhere the system entropy approaches zero, and E is an energy term of the order of bond rotational barriers. The Vogel-Fulcher equation has been used successfully in studies9J9-22to describe the temperature dependence of dielectric and mechanical relaxation times of homopolymers as well as of polymer blends and solutions. The apparent relaxation times z* of the substituted polyphenylenes from dielectric frequency plane measurements are presented in Figure 5 in an Arrhenius-type plot together with the best fits t o the Vogel-Fulcher equation. The behavior of BPA-PC which is known t o have high intramolecular bond rotational barriers is also plotted in Figure 5 for comparison. The Vogel-Fulcher parameters of the best fit curves in Figure 5 are listed in Table 3. Although it exhibits the lowest Tg and hence the lowest TOof the three polyphenylenes, PX-2000 displays the highest Vogel energy E. Considering the size of the 4-phenoxybenzoyl group compared to a benzoyl group, it would be expected that the bond rotational barrier around the main chain phenylene segment in PX-2000 would be larger than PX-1000 or P-1. The WLF constants C1 and C2 at TR obtained from viscoelastic measurements may be recalculated for the glass transition temperature Tgobtained from volumetric or calorimetric measurement^:^^

sample

PX-2000

log t 0 Q

E"

(s)

(kJ/mol)

-11.6 f 0.3 14.3 f 1.2 PX-1000 -10.8 0.6 10.6 f 1.8 P-1 -11.5 f 0.4 11.8 1.4 BPA-PC -12.9 f 0.8 9.0 1.7

*

*

Toa ("C) 74.8 f 4.0 92.6 f 6.7 104.0 f 4.9 100.2 f 4.8

(5*

R 0.9999 0.9993 0.9996 0.9995

T, 1 s)b

=

("0 140 144 157 139

a Determined by fitting the Vogel-Fulcher equation (eq 2) to the data in Figure 5. Calculated from the Vogel-Fulcher equation using the parameters listed above.

ClgC2g

c, = c2g

+ TR - Tg

where C1, and Czg are the new WLF constants at Tg. Using the observation that TO= Tg - Czg, the WLF equation can be rewritten to include the Vogel temperature:

(4) Therefore, by definition, the WLF shift factor UT diverges to infinity when T = TO.The apparent activation energy (E,) of a viscoelastic relaxation follows a distinctly non-Arrhenius temperature d e p e n d e n ~ e : ~ ~

E, =

2. 303RC,,Cz,~ (CZg+ T - TgI2

or

at T = Tg. Since at high temperatures each molecular segment relaxes independently, the primitive activation energy E associated with local bond rotational barriers is

E = 2.303RClgC2,

(5c)

equivalent t o the activation energy of noncooperative intramolecular bond rotation Ap* used by M a t ~ u o k a ~ ~ where Ap*lk = llaf.



Table 4. WLF and Vogel-Fulcher Parameters at T, for Poly-X Mechanical Relaxation Behavior

sample PX-2000 PX-1000 P-1

Aaa ("C-l) (f0.15) 5.15 3.09 2.33

Tga ("C) kt0.5) 156.5 159.2 160.7

Cl,b (f0.6)

C22 (K) (f1.8)

11.1

94.6 82.8 60.8

11.9 10.5

Toc("C) (12.5) 61.9 76.4 99.9

Ec (kJ/mol) (f1.3) 20.1 18.9 12.3

Ea(TgF (kJ/mol) (f35) 414 514

622

Measured by TMA at 10 "C/min [Aa = a(1iquid) - a(g1ass)l. Calculated from eqs 3a and 3b. TO= Tg - Cpg and E = 2.303RC&zg Calculated from eq 5b using T gby TMA.

(eq 5c).

1

4.0 --

-

l

l

l

~

r

l

I

l

~

l

l

l

l

~

l

l

l

l

Normalize with Tgat which log a,= 5.0 from WLF fit

2.0 0.0

-2.0 -4.0

0.80

0.85

0.90 T,/T

0.95

1.oo

Figure 6. Cooperativity plot of (a) dielectric relaxation times t* and (b) WLF shift factors UT for Poly-X polyphenylenes.

Using eqs 3-5, TO,E , and E,(T,) were calculated (Table 4) for each of the Poly-X polyphenylenes from the WLF parameters in Table 2. Although there are quantitative differences between both the Vogel energies and the Vogel temperatures (Tables 3 and 4), a consistent trend is observed. PX-2000 exhibits the highest intramolecular bond rotational barrier and lowest TO while P-1 displays the lowest Vogel energy and highest TO.The differences between the viscoelastic and dielectric Vogel parameters may be explained by the different domain sizes of the experimental probes. Since dielectric measurements examine the mobility of dipolar

molecular segments, the experimental domain size is on the order of monomer units while viscoelastic experiments reveal relaxations of 5-10 repeat units. Ngailg has discussed the correlation between viscoelastic, dielectric, and dynamic light scattering relaxation times in this manner. The effect of molecular structure on the temperature dependence of relaxation times is not obvious from the shift factor or z* data (Figures 4 and 5). Roland and co-workers8-10,21have attempted to show that a correlation exists between the shape of the viscoelastic or dielectric relaxation spectrum and the temperature

Macromolecules, Vol. 28, No. 6,1995


1.o

0.8

0.6 194 198

0.4 t

msr

0.2 0.0

-

Poly(4'-phenoxybenzoy1-1,4-phenylene) 0.0

,

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

'

1

1

1

1

1

1

1

'

1

1

1

1

1

1

1

0

0.8

0 0

0.6 A A

0.4 0.2

3

1

1

175 180 183 187 190 193

197 200 203

Poly [(benzoyl-l,4-phenylene)-

co-(l,3-phenylene)] 0.0 ---

-3.0 -2.0 -1.0 0.0 1.0 2.0 log (f/f"d

3.0

4.0

Figure 7. Reduced dielectric loss ( E ' ' / / E ' ' ~ ~ ~mastercurves ) for (a) PX-1000, (b) PX-2000, and (c) P-1where fmax is the frequency a t the dielectric loss maximum

dependence of relaxation times. In their coupling model of relaxation, Roland and co-workers have proposed that t* is determined not only by the local friction coefficient

(as in free volume concepts of relaxation) but also by the extent of intermolecular cooperative rearrangements. AngellZ5introduced the convenient representa-


Macromolecules, Vol. 28, No. 6,1995

temperature-dependent relaxation time, and /3 is the “stretched” exponential factor which indicates the distribution of relaxation times. When B = 1, eq 6 represents a simple Debye-type relaxation. In the coupling model of Roland et aZ,,9Jo,21 the Kww /3 parameter is equal to 1 - n where n represents the coupling parameter and is said to indicate the strength of intermolecular cooperative rearrangements. Hence, the relaxation spectrum will broaden as the coupling parameter increases. Weiss and ~ o - w o r k e r s ~have ~J~ expressed the dielectric loss function as

C 0

. I

(P

X

(P

I

2

c 1.0 1 , 160

’ ’ ’

’’

’ ’ ’

’’

4

’ ‘ ’

2

’ ’ ’

I

’ ’ ’

A 0.3

180 190 200 210 Temperature (“C) Figure 8. Temperature dependence of Poly-X dielectric relaxation strength AE and KWW stretched exponential parameter p. 170

20 n

E 15

i C

10

0

. I

8

5

W

0 100

120

140

160

180

Temperature (“C)

200

tion of aT or z* data in terms of a normalized temperature 2’42‘using an arbitrary glass transition temperature Tgoutside the measurement range t o scale the data appropriately. In such “fragility” or “cooperativity” plots, materials which exhibit greater temperature sensitivity of aT or z* will possess a greater degree of intermolecular cooperative motion. The experimental shift factor and dielectric relaxation data for the three polyphenylenes are replotted in Figure 6 in the form of a cooperativity plot. As suggested by the fits of this data to the Vogel-Fulcher and WLF equations discussed earlier, the viscoelastic and dielectric relaxation times possess a similar temperature dependence. This observation implies that both methods examine the same relaxation mechanism, albeit on a different length scale. These cooperativity plots also suggest that the degree of intermolecular cooperative motion is greatest in P-1 since it displays the most pronounced temperature sensitivity of aT and z*. To examine more closely the nature of cooperative motion in the Poly-X resins, we have analyzed the shape of the dielectric relaxation spectrum. Many studies have proved that the empirical Kolrausch-WilliamsWatts (KWW) equation?

o 5 ,t?5 1

(7a)

--hm exp(-u?

(7b)

with Q,(z> = 1

cos(zu) du

where AE is the dielectric relaxation strength, z = ut*, and w = 2nf. They have developed a computational method to solve the ”stable”probability density function Qa(z) over a wide range of /3 and z. Using this algorithm, we have calculated Ac and /? for the Poly-X polyphenylenes. The normalized dielectric loss spectrum of each of the Poly-X polyphenylenes over a wide temperature range is plotted versus normalized frequency in Figure 7. Comparing the three data sets, there appears to be little variation in the KWW factor /3 at any temperature since the shapes of the loss curves are almost identical. The relaxation strength Ac and KWW factor p for each sample and at all temperatures have been plotted in Figure 8. According to FrOlichz7

Ac = ,ue2/T

Figure 9. Thermal expansion curves of Poly-X resins.

4(t>= exp(-t/t*Y

E”(w) = Acz*Q,(z)

(6)

can be used to accurately fit the dielectric and mechanical loss spectra of many polymers in the vicinity of the glass transition temperature. In this expression, &(t) is the dipole moment correlation function, z* is the

(8)

where pe is the effective dipole moment per repeat unit. As expected, the relaxation strength for each sample was found to be inversely proportional to temperature and the relative magnitude of A6 varied according to the dipole moment of the repeat unit, as seen in the thermal scans of the substituted polyphenylenes. Within the experimental error of f0.02,the stretched exponential term /3 was nearly constant over the temperature range studied. Only a very weak dependence of p on the chemical structure of the polyphenylene was observed. Since B varies only from 0.42 to 0.46 over all temperatures and structures, the corresponding coupling parameter ( n = 1- p) varies in the narrow range from 0.54 to 0.58. As discussed previously, an increase in the “fragility”,i.e., the temperature dependence of the relaxation times, should be accompanied by a corresponding increase of intermolecular coupling. For example, in a homologous series of polybutadienes, Roland and Ngaig concluded that the content of vinyl groups correlated with the broadening of the viscoelastic relaxation spectra, Le., the increase of intermolecular coupling and with the ”fragility”of the polymers. Since the coupling parameter n varied only slightly in this study with molecular structure, the temperature dependence of relaxation times for the Poly-X polyphenylenes may not be fully explained by the coupling model. The free volume theory is a straightforward approach which has been used more often than the coupling model to describe segmental relaxation dynamics. From this perspective, the molecular mobility a t any temperature is controlled by the free volume or the unoccupied



-

0.10

3 4)

0.08 n

+ 0

0.06

4) 4)

k

0.04

I

Q E 0

0.00 2.20

8

-

&

I

2.00

Q

E“ 0 (cpp

:G

1.80

e,a

O 1.40 + a

*I I

0

1.00 0.85

0.90

TJT

0.95

1.oo

Figure 10. (a) Fractional free volume f and (b) normalized fractional free volume flf, versus reduced temperature for Poly-X polyphenylenes. (The straight lines represent the initial slope of the normalized free volume.)

volume between chains. The onset of a glass transition is determined by a reduction in the rate of free volume collapse as the temperature is lowered. The traditionally vague concept of fractional free volume f has been defined as Vflg where Vf and Vg are the free volumes at any temperature T and Tg,respectively. Ferryz3has assumed that the fractional free volume increases linearly with temperature as

f = fg

+ cq(T - T g )

(9a)

However, neither f nor afmay be determined by direct experimental methods. Assuming that afequals Aa, the difference between the macroscopic expansion coefthe ficients of the liquid a1 and glassy ag fractional free volume at Tg(fg) and fmay be calculated as follows: fg

= CzgAa

(9b)

and

f = Aa(C,,

+ T - Tg)

(9c)

The thermal expansion curves for the substituted polyphenylenes are shown in Figure 9. Although the expansion coefficients in the glassy state are similar, PX-2000clearly exhibits a much higher value of a1 than PX-1000or P-1.On the basis of eq 9b, the fractional free volume at Tgof PX-2000was found t o be twice that of PX-1000and more than 3 times that of P-1. Since Tgis inversely proportional to free volume, this observation is consistent with the dynamic mechanical and dielectric thermal scans a t fixed frequency discussed above in which the T g increased from PX-2000to PX1000 to P-1.When viewed in a normalized temperature format (Figure loa), the rate of free volume expansion with temperature is greatest for PX-2000and smallest for P-1.Considering only the total free volume, it might be expected that PX-2000would display the greatest “fragility” of these polyphenylenes. However, the temperature dependence of aT and t* scales not with the total free volume but with the relative change in free volume over the temperature range of interest. As shown in Figure lob, the normalized free volume of P-1 increases at a greater rate with increasing temperature than that of PX-1000or PX-2000.This difference may

Macromolecules, Vol. 28, No. 6, 1995 be explained by the main chain flexibility of P-1 due to incorporation of rn-phenylene segments. As temperathe rigid-rod character of PXture increases above Tg, 1000 and PX-2000 restricts free volume expansion to librations and rotations of the side groups around the main chain while the m-phenylene kink units in P-1 allow for long range diffusive mobility and main chain segmental motion with a large swept volume. Since the intermolecular coupling parameter n varies only within experimental error as a function of molecular structure, an alternate explanation of the fragility of the polyphenylenes is necessary. The differences in the temperature dependence of relaxation times of the Poly-X resins can be explained in a straightforward manner by the relative change of free volume with temperature in each of the substituted poly@-phenylenes).

IV. Conclusions Poly@-phenylene) resins containing benzoyl and 4phenoxybenzoyl side groups display flexural moduli approaching 10 GPa and glass transition temperatures above 150 “Cas well as low dielectric constants and low dielectric loss under ambient conditions. As shown by dynamic mechanical and expansion coefficient measurements, the Tgof these polymers varies with free volume. The 4-phenoxybenzoyl-substitutedpolyphenylene exhibits the lowest Tgand largest free volume but displays the highest intramolecular bond rotational barrier due the bulkiness of the side group. The temperature dependence of dielectric and viscoelastic relaxation times in these substituted polyphenylenes can be explained by simple free volume considerations. The “fragility”or temperature sensitivity of relaxation times correlates not with total free volume but with the relative change in free volume with respect t o the free volume at Tg.

Acknowledgment. We thank Drs. John Bendler and Andrea Schmitz of General Electric Corp. for their computer program for calculating KWW relaxation spectra and Professor Paul Lahti for the use of his Silicon Graphics workstation. This work was supported by Air Force Office of Scientific Research Grant 94-01. References and Notes (1) Rehahn, M.; Schluter, A. D.; Wegner, G.; Feast, W. J. Polymer

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(23) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980; pp 287 & 289. (24) Matsuoka, S. Relaxation Phenomena in Polymers; Hanser: New York, 1992. (25) Angell, C. A. J . Non-Cryst. Solids 1991,131-133, 13. (26) Williams, G.; Watts, D. C. Trans. Faraday SOC.1970,66, 2503. (27) Frolich, H. Theory of Dielectrics; Oxford University Press: London, 1958. (28) Bueche, F. J . Chem. Phys. 1953,21,1850. (29) Fox, T. G.; Flory, P. J. J . Appl. Phys. 1950,21,581. (30) Fox, T. G.; Flory, P. J . J . Polym. Sci. 1954,14,315.

MA945019Z

Viscoelastic and Dielectric Relaxation Behavior of Substituted Poly(p

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